What are identities and how do you use them

We know sin(30) = 1/2, so cos(60) = 1/2 as well.

We can also combine identities to make other identities. For example, we can take the angle sum formula for sin, i.e. sin(x + y) = sin(x)cos(y) + cos(x)sin(y), and turn it into the double angle sum formula, i.e. an expansion for sin(2x) in terms of sin(x) and cos(x). How do we do this? Well, if we just keep x the same and substitute y = x in the identity, we obtain:

sin(x + x) = sin(x)cos(x) + cos(x)sin(x)
sin(2x) = 2sin(x)cos(x)

Now, given any x, we know that the angle sum formula works for x = x and y = x, which produces the above expression, and hence is therefore true. So, given any x, the above is true, i.e. it is an identity.

So yeah, that's identities: what is, how to use, and why you should have started study a lot earlier. Good luck.

EDIT: "I think I should do fine"

I'm genuinely relieved to hear that. Still, good luck anyway. ;-)